On average, the Pacific ocean is 13,740 feet deep. Using a little bit of math (and Google), I found that, on average, the pressure of water per square inch, is approximately 15lbs per 33 feet. (sorry for those who like Metric, I'm just using what I know.) So, with that, I calculated that at 13,000 feet down, the pressure of the water is 5909 lbs per square inch. So for every inch of the Chief facing outwards, he'd be experiencing nearly 6 tons of pressure. I can't even begin to describe how much pressure that is. Imagine the entire weight of a Ford Explorer (truck, about 6000lbs) compressed into a 1 inch cube. Now imagine hundreds of those pressing down on the Chief. And that's not even the pressure exerted on his sides. Sorry, but I really doubt he could survive that if he still dies to bullets and plasma fire. Shields would cave, as it'd be like the weight of a scorpion tank (or 10) on all sides, his visor would crack, and he'd be dead long before he hit the bottom.
Did I work way too hard on that?
Edit: Ooh ooh, more compelling analogy. Imagine the Chief laying down, and there's a scorpion tank right over him facing downward so one of the tread guards is right in front of his face. And drop. Now imagine that happening to every part of his body at once. Repeatedly.